Question

Solve $\int \cot x\log \sin xdx$

Answer 1

$\int \cot x\log \sin xdx$

Put, $\log \sin x=t$

$⟹\frac{1}{\sin x}\cos xdx=dt$

$⟹\cot xdx=dt$

Now, $\int \cot x\log \sin xdx=\int tdt$

$=\frac{t^2}{2}+c$

$=\frac{(\log \sin x{)}^2}{2}+c$